Final answer:
The resonant frequency of an RLC circuit is found by the formula fo = 1 / (2π√(LC)), where L is the inductance and C is the capacitance. It is the frequency at which the circuit naturally oscillates with maximum current and minimum impedance, assuming no external driving voltage source.
Step-by-step explanation:
The resonant frequency (fo) of an RLC circuit is achieved when the inductive and capacitive reactances are equal and opposite in phase, cancelling each other out. At this point, the circuit oscillates at its natural frequency if undriven by an external voltage source and the impedance is solely resistive (Z=R), resulting in the maximum current (Irms).
To find the resonant frequency, we can use the formula fo = 1 / (2π√(LC)), where L is the inductance and C is the capacitance of the circuit. The inclusion of the resistor (R) does not affect the resonant frequency directly, but rather the sharpness and the height of the peak current at resonance. The formula indicates that resonant frequency depends solely on the values of L and C.
For the specific values provided, such as L = 2.0 mH and C = 25μF, we substitute them into the formula to calculate fo. For example, if a question asked for the resonant frequency of a circuit given R = 100 ohms, L = 2.0 H, and C = 5.0μF, we would use the given L and C values to calculate fo accordingly.